Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Who Owns the Future? is his visionary reckoning with the most urgent economic and social trend of our age: the poisonous concentration of money and power in our digital networks.Lanier has predicted how technology will transform our humanity for decades, and his insight has never been more urgently needed. He shows how Siren Servers, which exploit big data and the free sharing of information, led our economy into recession, imperiled personal privacy, and hollowed out the middle class. The networks that define our world—including social media, financial institutions, and intelligence agencies—now threaten to destroy it.But there is an alternative. In this provocative, poetic, and deeply humane book, Lanier charts a path toward a brighter future: an information economy that rewards ordinary people for what they do and share on the web.

    Now he gathers the best of his best, updated and expanded upon, to guide readers on a mind-bending tour of the far frontier, and how these advances are radically transforming our lives. From the ways science and technology are fundamentally altering our bodies and our world (the world’s first bionic soldier, the future of evolution) to those explosive collisions between science and culture (life extension and bioweapons), we’re crossing moral and ethical lines we’ve never faced before.As Kotler writes, “Life is tricky sport—and that's the emotional core of this story, the real reason we can’t put Pandora back in the box. When you strip everything else away, technology is nothing more than the promise of an easier tomorrow. It’s the promise of hope. And how do you stop hope?”Join Kotler in this fascinating exploration of our incredible next: a deep dive into those future technologies happening now—and what it means to be a part of this brave new world.

    Most know Richard Feynman for the hilarious anecdotes and exploits in his best-selling books Surely You're Joking, Mr. Feynman! and What DoYou Care What Other People Think? But not always obvious in those stories was his brilliance as a pure scientist—one of the century's greatest physicists. With this book and CD, we hear the voice of the great Feynman in all his ingenuity, insight, and acumen for argument. This breathtaking lecture—"The Motion of the Planets Around the Sun"—uses nothing more advanced than high-school geometry to explain why the planets orbit the sun elliptically rather than in perfect circles, and conclusively demonstrates the astonishing fact that has mystified and intrigued thinkers since Newton: Nature obeys mathematics. David and Judith Goodstein give us a beautifully written short memoir of life with Feynman, provide meticulous commentary on the lecture itself, and relate the exciting story of their effort to chase down one of Feynman's most original and scintillating lectures.

    In The History of the Future, Harris once again deep-dives into a tech drama for the ages to expertly tell the larger-than-life true story of Oculus, the virtual reality company founded in 2012 that—less than two years later—would catch the attention of Mark Zuckerberg and wind up being bought by Facebook for over $2 billion dollars.This incredible underdog story begins with inventor Palmer Luckey, then just a nineteen-year-old dreamer, living alone in a camper trailer in Long Beach, California. At the time, virtual reality—long-hailed as the ultimate technology—was so costly and experimental that it was unattainable outside of a few research labs and military training facilities. But with the founding of Oculus, and the belief that his tantalizing vision of the future could one day be more than science fiction, Luckey put everything he had into creating a device that would allow gamers like him to step into virtual worlds and, in doing so, hopefully kickstart a VR revolution. With the help of an industry legend, a serial entrepreneur, and a slew of colorful characters—including those behind gaming sensations like Doom, Words with Friends, and Guitar Hero—Luckey’s scrappy startup would finally deliver the dream of immersive and affordable virtual reality to consumers, leading geeks and gamers to be excited in a way that they hadn’t been in years, and tech firms and investors scrambling to get in on the action before it was too late.Over the course of three years (and with unprecedented access from Oculus and Facebook), Harris conducted hundreds of interviews with key players in the VR revolution—including Luckey, his partners, and their cult of dreamers—to weave together a rich, cinematic narrative that captures the breakthroughs, breakdowns, and human drama of trying to change the world. The result is a supremely accessible, entertaining look at the birth of a new multi-billion-dollar industry; one full of heroes, villains, and twists at every corner. Take, for instance, Harris’ own discovery while writing this story. When he started this endeavor, he had no idea that this tale would somehow involve Donald Trump, billion-dollar lawsuits, illegal practices, and end with Luckey—eventually ousted from Facebook—as one of the most polarizing figures in Silicon Valley.

    Every new reader's brain possesses the extraordinary capacity to rearrange itself beyond its original abilities in order to understand written symbols. But how does the brain learn to read? As world-renowned cognitive neuroscientist and scholar of reading Maryanne Wolf explains in this impassioned book, we taught our brain to read only a few thousand years ago, and in the process changed the intellectual evolution of our species.Wolf tells us that the brain that examined tiny clay tablets in the cuneiform script of the Sumerians is configured differently from the brain that reads alphabets or of one literate in today's technology.There are critical implications to such an evolving brain. Just as writing reduced the need for memory, the proliferation of information and the particular requirements of digital culture may short-circuit some of written language's unique contributions—with potentially profound consequences for our future.Turning her attention to the development of the individual reading brain, Wolf draws on her expertise in dyslexia to investigate what happens when the brain finds it difficult to read. Interweaving her vast knowledge of neuroscience, psychology, literature, and linguistics, Wolf takes the reader from the brains of a pre-literate Homer to a literacy-ambivalent Plato, from an infant listening to Goodnight Moon to an expert reader of Proust, and finally to an often misunderstood child with dyslexia whose gifts may be as real as the challenges he or she faces.As we come to appreciate how the evolution and development of reading have changed the very arrangement of our brain and our intellectual life, we begin to realize with ever greater comprehension that we truly are what we read. Ambitious, provocative, and rich with examples, Proust and the Squid celebrates reading, one of the single most remarkable inventions in history. Once embarked on this magnificent story of the reading brain, you will never again take for granted your ability to absorb the written word.

    To the right listener, they tell us all about themselves: where they came from, how they lived, how they died - and who killed them. Forensic scientists can unlock the mysteries of the past and help justice to be done using the messages left by a corpse, a crime scene or the faintest of human traces. Forensics uncovers the secrets of forensic medicine, drawing on interviews with top-level professionals, ground-breaking research and Val McDermid's own experience to lay bare the secrets of this fascinating science. And, along the way, she wonders at how maggots collected from a corpse can help determine time of death, how a DNA trace a millionth the size of a grain of salt can be used to convict a killer and how a team of young Argentine scientists led by a maverick American anthropologist uncovered the victims of a genocide.In her crime novels, Val McDermid has been solving complex crimes and confronting unimaginable evil for years. Now, she's looking at the people who do it for real, and real crime scenes. It's a journey that will take her to war zones, fire scenes and autopsy suites, and bring her into contact with extraordinary bravery and wickedness, as she traces the history of forensics from its earliest beginnings to the cutting-edge science of the modern day.

    The science of complexity studies how single elements, such as a species or a stock, spontaneously organize into complicated structures like ecosystems and economies; stars become galaxies, and snowflakes avalanches almost as if these systems were obeying a hidden yearning for order. Drawing from diverse fields, scientific luminaries such as Nobel Laureates Murray Gell-Mann and Kenneth Arrow are studying complexity at a think tank called The Santa Fe Institute. The revolutionary new discoveries researchers have made there could change the face of every science from biology to cosmology to economics. M. Mitchell Waldrop's groundbreaking bestseller takes readers into the hearts and minds of these scientists to tell the story behind this scientific revolution as it unfolds.

    While not every story is concerned with the hard science behind space travel and other futuristic ventures, fiction can give listeners an amazing insight into what people could be capable of and what people dream of doing.In the 10 lectures of The Science of Sci-Fi: From Warp Speed to Interstellar Travel, Professor Erin Macdonald interweaves real science and the achievements of the imagination to reveal the truth that underlies favorite stories and sheds light on what the future may hold. From faster-than-light travel to journeys through time itself, science fiction makes humanity seem limitless. So, what scientific boundaries are people pushing against while seeking to fly among the stars?Listening Length: 3 hours and 59 minutes

    Called the Pope by his peers, he was regarded as infallible in his instincts and research. His discoveries changed our world; they led to weapons of mass destruction and conversely to life-saving medical interventions.This unassuming man struggled with issues relevant today, such as the threat of nuclear annihilation and the relationship of science to politics. Fleeing Fascism and anti-Semitism, Fermi became a leading figure in America's most secret project: building the atomic bomb. The last physicist who mastered all branches of the discipline, Fermi was a rare mixture of theorist and experimentalist. His rich legacy encompasses key advances in fields as diverse as comic rays, nuclear technology, and early computers.In their revealing book, The Pope of Physics, Gino Segré and Bettina Hoerlin bring this scientific visionary to life. An examination of the human dramas that touched Fermi’s life as well as a thrilling history of scientific innovation in the twentieth century, this is the comprehensive biography that Fermi deserves.

    Unlike their human counterparts, who must alter their environment to accommodate our physical limitations, animals are adaptable to an amazing range of conditions--i.e., radical changes in a creature's physiology take place to match the demands of the environment. Winter provides an especially remarkable situation, because of how drastically it affects the most elemental component of all life: water.Examining everything from food sources in the extremely barren winter landscape to the chemical composition that allows certain creatures to survive, Heinrich's Winter World awakens the largely undiscovered mysteries by which nature sustains herself through the harsh, cruel exigencies of winters

    From blonde to ginger, the brown that changed the way battles were fought to the white that protected against the plague, Picasso's blue period to the charcoal on the cave walls at Lascaux, acid yellow to kelly green, and from scarlet women to imperial purple, these surprising stories run like a bright thread throughout history.In this book, Kassia St. Clair has turned her lifelong obsession with colors and where they come from (whether Van Gogh's chrome yellow sunflowers or punk's fluorescent pink) into a unique study of human civilization. Across fashion and politics, art and war, the secret lives of color tell the vivid story of our culture.

    The fantastic journey began in 1977, before the first episode of Cosmos aired. The mission was planned as a grand tour beyond the moon; beyond Mars, Jupiter, and Saturn; and maybe even into interstellar space. The fact that it actually happened makes this humanity's greatest space mission.In The Interstellar Age, award-winning planetary scientist Jim Bell reveals what drove and continues to drive the members of this extraordinary team, including Ed Stone, Voyager's chief scientist and the one-time head of NASA's Jet Propulsion Lab; Charley Kohlhase, an orbital dynamics engineer who helped to design many of the critical slingshot maneuvers around planets that enabled the Voyagers to travel so far; and the geologist whose Earth-bound experience would prove of little help in interpreting the strange new landscapes revealed in the Voyagers' astoundingly clear images of moons and planets.Speeding through space at a mind-bending eleven miles a second, Voyager 1 is now beyond our solar system's planets. It carries with it artifacts of human civilization. By the time Voyager passes its first star in about 40,000 years, the gold record on the spacecraft, containing various music and images including Chuck Berry's "Johnny B. Goode," will still be playable.

    Einstein famously quipped that God does not play dice with the universe, and Schrödinger is equally well known for his thought experiment about the cat in the box who ends up “spread out” in a probabilistic state, neither wholly alive nor wholly dead. Both of these famous images arose from these two men’s dissatisfaction with quantum weirdness and with their assertion that underneath it all, there must be some essentially deterministic world. Even though it was Einstein’s own theories that made quantum mechanics possible, both he and Schrödinger could not bear the idea that the universe was, at its most fundamental level, random.As the Second World War raged, both men struggled to produce a theory that would describe in full the universe’s ultimate design, first as collaborators, then as competitors. They both ultimately failed in their search for a Grand Unified Theory—not only because quantum mechanics is true, but because Einstein and Schrödinger were also missing a key component: of the four forces we recognize today (gravity, electromagnetism, the weak force, and the strong force), only gravity and electromagnetism were known at the time.Despite their failures, though, much of modern physics remains focused on the search for a Grand Unified Theory. As Halpern explains, the recent discovery of the Higgs Boson makes the Standard Model—the closest thing we have to a unified theory—nearly complete. And while Einstein and Schrödinger tried and failed to explain everything in the cosmos through pure geometry, the development of string theory has, in its own quantum way, brought this idea back into vogue. As in so many things, even when he was wrong, Einstein couldn’t help but be right.

    The human brain has some capabilities that the brains of other animals lack. It is to these distinctive capabilities that our species owes its dominant position. If machine brains surpassed human brains in general intelligence, then this new superintelligence could become extremely powerful--possibly beyond our control. As the fate of the gorillas now depends more on humans than on the species itself, so would the fate of humankind depend on the actions of the machine superintelligence.But we have one advantage: we get to make the first move. Will it be possible to construct a seed Artificial Intelligence, to engineer initial conditions so as to make an intelligence explosion survivable? How could one achieve a controlled detonation?